Solve for $x$ and $y$ using elimination. $\begin{align*}x+5y &= -9 \\ 2x-9y &= 1\end{align*}$
Answer: We can eliminate $x$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-2$ and the bottom equation by $1$ $\begin{align*}-2x-10y &= 18\\ 2x-9y &= 1\end{align*}$ Add the top and bottom equations. $-19y = 19$ Divide both sides by $-19$ and reduce as necessary. $y = -1$ Substitute $-1$ for $y$ in the top equation. $x+5( -1) = -9$ $x-5 = -9$ $x = -4$ The solution is $\enspace x = -4, \enspace y = -1$.